12.18.10 problem section 9.2, problem 10

Internal problem ID [2124]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 9 Introduction to Linear Higher Order Equations. Section 9.2. constant coefficient. Page 483
Problem number : section 9.2, problem 10
Date solved : Saturday, March 29, 2025 at 11:49:05 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+12 y^{\prime \prime }+36 y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 29

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+12*diff(diff(y(x),x),x)+36*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_4 x +c_2 \right ) \cos \left (\sqrt {6}\, x \right )+\sin \left (\sqrt {6}\, x \right ) \left (c_3 x +c_1 \right ) \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 38

ode=D[y[x],{x,4}]+12*D[y[x],{x,2}]+36*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to (c_2 x+c_1) \cos \left (\sqrt {6} x\right )+(c_4 x+c_3) \sin \left (\sqrt {6} x\right ) \]

✓ Sympy. Time used: 0.088 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(36*y(x) + 12*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} + C_{2} x\right ) \sin {\left (\sqrt {6} x \right )} + \left (C_{3} + C_{4} x\right ) \cos {\left (\sqrt {6} x \right )} \]